A multidimensional superposition principle: Classical solitons II

A concept introduced previously as an approach for finding superposition formulae for solutions of nonlinear PDEs and an explanation of various types of wave interactions in such systems is developed further, both from the theoretical and technical point of view. In its framework, which is the framework of the multidimensional superposition principle, a straightforward and self-consistent technique for constructing the related invariant manifolds in a soliton case is proposed. The method is illustrated by simple examples, which, in particular, show in principle the generality that exists between superposition formulae for conventional linear and nonlinear soliton equations. The demonstration that the so-called truncated singular expansions associated can be with some sort of the above soliton invariant manifolds is also presented.